We propose here a new transport mechanism based on variable-range hopping between power-law localised states. It is shown to be the dominant mechanism at low temperatures. We also argue that a diffusive-hopping transition occurs above the mobility edge, at which the negative magnetoresistance is expected to vanish. Recent data on Si inversion layers support the assertion that such a transition exists and the negative magnetoresistance is found to vanish at a temperature of about 0.3 K for an electron density n ≈ 0.7 X 1016 m-2, whereas the mobilityedge isestimated to occurfor n > (0.4-0.5) x 1016 m-2. We also examine the possibility of the absence of a mobility edge and study two hopping mechanisms involving exponentially localised states, for n > 0.7 x 1016 m-2. We present evidence that such mechanisms are not involved here and conclude that exponentially localised states cannot exist for n > 0.7 x 1016 m-2. We show that the data are in agreement with our predictions, which follow from the existence of a mobility edge separating exponentially localised states from power-law localised states.